Spontaneous synchronization is a common phenomenon - from walkers pacing in time to the development of rhythmic applause at rally and concerts. But it isn't always good. Can you disrupt the system by placing a few "contrarians" in the crowd? It turns out to be possible.

It is remarkable how easily a group of independent but interacting agents can fall into sync without the need for a single leader. Sometimes this is a good thing, but often it is a problem - think people walking over a bridge in lock step or routers getting in transmission sync so bringing the network down. When a neural network falls into synchronicity then the result is usually a seizure.

If we can prevent such events then it might be possible to build a brain "pacemaker" that can disrupt such synchronization. Similarly, we could deploy the mechanism to stop structures collapsing because of resonance or perhaps alter the outcome of a political rally by suppressing the synchronized clapping that even the less-approving join in.

But how best to do it?

Can the mechanism that brings agents into sync be spoiled by the insertion of just a few contrarian agents who attempt to break time with the rest of the group?

This is a question that has recently received some attention from researchers in the physics department at ETH Honggerber (Switzerland) and Universidade Federal do Ceara (Brazil) and the results are fascinating.

The standard model for analyzing spontaneous synchronicity is the Kuramoto model. This has a collection of agents performing some act at a specific frequency. Over time the frequency is influenced by the phase difference between the agent and a set of neighboring agents. The strength of the interaction is controlled by a coupling parameter λ. When λ is small the frequencies remain spread out and uncorrelated, but as soon as it exceeds a threshold the agents quickly come into synchronicity.

If you would like to see this in action take a look at the following video which shows a polar plot of oscillators with frequency as the radius and phase as the polar angle. You can see how quickly they synchronize:

The new work adds a small number of contrarians which change their frequency in the opposite direction from the rest of the group. Two strategies were tested - one involved moving the contrarians away from the overall mean frequency and the other simply moved them away from the frequencies of their neighbors.

You might think that a contrarian using average frequency would disrupt the synchronization more readily as it is using global information - but no. It turns out that, instead of disrupting the synchronization, it introduces an additional cyclic behavior with the synchronization frequency flipping between two phases.

The contrarians using only local information were remarkably effective. If you add around 5% contrarians then the synchronization effect is completely disrupted. You can see this in the graphs below

The first graph shows what happens when the contrarians react to the mean frequency and phase. As the coupling constant is increased, the measure of coherence r suddenly increases at about 0.2. In other words, the contrarians using global information have little effect.

The second chart shows what happens when they react to their neighbor's frequency and phase - i.e. when they only use local information. Each of the colored lines is for a different proportion of contrarians. You can see that for small proportions there is still a big effect and when the proportion is around 0.2 there is no evidence of the spontaneous synchronization.

What all this means is that with a small number of contrarians reacting only to their nearest neighbors you can disrupt the synchronization.

The paper goes on to demonstrate the disruptive effect in some real networks including the neural network of a small worm and a network of routers. In each case the results demonstrated that it was possible to use a small number of contrarians to disrupt the synchronicity.

The study opens up new possibilities in parallel distributed algorithms and demonstrates that it is not only possible to create synchronicity without a master conductor you can also prevent it using agents that use only local information.

So if you want to influence a crowd, simply introduce a small number of people trained to clap out of sync with their neighbors.

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